If the loudness of a sound increases by 6 dB, find the percentage change in the intensity of the sound, give your answer correct to 3 significant figures.
[The relation between the loudness (D dB) of a sound and its intensity (I unit) can be expressed as D = 10 log(10^12 I) ]
F.4 logarithmic functions2
2010-04-19 6:16 am
回答 (1)
2010-04-19 3:26 pm
✔ 最佳答案
Let 10^12 = kD = 10 log kI, where I is the original sound intensity.
D + 6 = 10 log kJ, where J is the new sound intensity.
(D + 6) - D = 10 log kJ - 10 log kI
6 = 10 log ( kJ/kI)
0.6 = log J/I
J/I = 3.981
so % change = (J - I)/I x 100% = (J/I - 1) x 100% = (3.981 - 1) x 100% = 298%
2010-04-19 07:28:00 補充：
Note : The value of k is not important.
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